Sorting in c log n parallel steps
Combinatorica
Asymptotically tight bounds on time-space trade-offs in a pebble game
Journal of the ACM (JACM)
Advances in Pebbling (Preliminary Version)
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Time-space tradeoffs for some algebraic problems
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
SCG '87 Proceedings of the third annual symposium on Computational geometry
Applications of combinatorial designs in computer science
ACM Computing Surveys (CSUR)
An O(logN) deterministic packet routing scheme
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
An O(log N) deterministic packet-routing scheme
Journal of the ACM (JACM)
Expanders that beat the eigenvalue bound: explicit construction and applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Superconcentrators of depths 2 and 3; odd levels help (rarely)
Journal of Computer and System Sciences
Multiple access communications using combinatorial designs
Theoretical aspects of computer science
Multiple Access Communications Using Combinatorial Designs
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
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Expanding graphs and superconcentrators are relevant to theoretical computer science in several ways. Here we use finite geometries to construct explicitly highly expanding graphs with essentially the smallest possible number of edges.Our graphs enable us to improve significantly previous results on a parallel sorting problem, by describing an explicit algorithm to sort n elements in k time units using &Ogr;(n&agr;k) processors, where, e.g., &agr;2 = 7/4.Using our graphs we can also construct efficient n-superconcentrators of limited depth. For example, we construct an n superconcentrator of depth 3 with &Ogr;(n4/3) edges; better than the previous known results.